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Question:
\(∫e^x secx(1+tanx)dx\) equals
\(∫e^x secx(1+tanx)dx\) equals
Updated On: Mar 1, 2024
\(e^xcosx+C\)
\(e^xsecx+C\)
\(e^xsinx+C\)
\(e^xtanx+C\)
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The Correct Option is A
Solution and Explanation
The correct answer isB: \(I=e^xsecx+C\)
\(∫e^x secx(1+tanx)dx\)
Let \(I=∫e^xsecx(1+tanx)dx=∫e^x(secx+secx\,tanx)dx\)
Also,let \(secx=ƒ(x)\,\,secx\,tanx=ƒ'(x)\)
It is known that,\(∫e^x[ƒ(x)+ƒ'(x)]dx=e^xƒ(x)+C\)
\(∴I=e^xsecx+C\)
Hence,the correct answer is B.
\(∫e^x secx(1+tanx)dx\)
Let \(I=∫e^xsecx(1+tanx)dx=∫e^x(secx+secx\,tanx)dx\)
Also,let \(secx=ƒ(x)\,\,secx\,tanx=ƒ'(x)\)
It is known that,\(∫e^x[ƒ(x)+ƒ'(x)]dx=e^xƒ(x)+C\)
\(∴I=e^xsecx+C\)
Hence,the correct answer is B.
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